Related papers: Novel approach for solving multipoint boundary val…
The six-vertex model with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is obtained. The kernel of the corrtesponding integral operator depends on Laguerre…
The Fredholm-Hammerstein integral equations (FHIEs) with weakly singular kernels exhibit multi-point singularity at the endpoints or boundaries. The dense discretized matrices result in high computational complexity when employing numerical…
We give the Jordan form and the Singular Value Decomposition for an integral operator ${\cal N}$ with a non-symmetric kernel $N(y,z)$. This is used to give solutions of Fredholm equations for non-symmetric kernels, and to determine the…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…
We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of…
The Legendre-based ultraspherical spectral method for ordinary differential equations is combined with a formula for the convolution of two Legendre series to produce a new technique for solving linear Fredholm and Volterra…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
Over the past few decades, kernel-based approximation methods had achieved astonishing success in solving different problems in the field of science and engineering. However, when employing the direct or standard method of performing…
This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems,…
In this article, we introduce a new class of coupled fractional Lane-Emden boundary value problems. We employ a novel approach, the fractional Haar wavelet collocation method with the Newton-Raphson method. We analyze the conditions in two…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
The drum problem-finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition-has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed. Boundary…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
We address the existence in the sense of sequences of solutions for a certain integro-differential type problem involving the logarithmic Laplacian. The argument is based on the fixed point technique when such equation contains the operator…
A trigonometric interpolation algorithm for non-periodic functions has been recently proposed and applied to study general ordinary differential equation (ODE). This paper enhances the algorithm to approximate functions in $2$-dim space.…
We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We…
We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic…
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…
This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…